Topological groups and invariant measures

Abstract

Lecture notes in Russian. Topics: the Haar measure (abstract theorems and explicit descriptions for different groups), measures on infinite-dimensional spaces with large natural groups of symmetries (Gaussian measures, Poisson measures, virtual permutations, inverse limits of unitary groups), zoo of examples of topological groups, generalities for large (infinite-dimensional) groups, polymorphisms.

Lecture notes in Russian

References in corpus (5)

• An overview of the Riemannian metrics on spaces of curves using the Hamiltonian approach
• Multi-operator colligations and multivariate characteristic functions
• Induced differential forms on manifolds of functions
• The space $L^2$ on semi-infinite Grassmannian over finite field
• On topologies on Lie braid groups